TECNOCIENCIA CHIHUAHUA, Vol. XIX (2025): enero-diciembre, e1874

https://revistascientificas.uach.mx/index.php/tecnociencia

ISSN-e: 2683-3360

Scientific Article

Dynamic Simulation of a Non-linear CSTR Using

Scilab/Xcos®: a Practical Approach for Chemical

Engineering Education

Simulación dinámica de un CSTR No Lineal usando Scilab/Xcos®: un

enfoque práctico para la enseñanza de la Ingeniería Química

*Correspondencia: Correo electrónico: ljuarezm@uach.mx (Luis Carlos Juárez-Martínez)

DOI: https://doi.org/10.54167/tch.v19i1.1874

Recibido: 13 de marzo de 2025; Aceptado: 30 de abril de 2025

Publicado por la Universidad Autónoma de Chihuahua, a través de la Dirección de Investigación y Posgrado.

Editor de Sección: Dr. Sergio Valle-Cervantes

Abstract

Understanding the dynamic behavior of chemical processes is essential for controlling industrial

operation, enhancing safety, and products quality. This work provides an accessible and practical

guide for students and educators to demonstrate the potential of Scilab/Xcos® as an open-source

alternative to MATLAB/Simulink®, for dynamic process simulation in chemical engineering

education. The study focuses on a non-linear Continuous Stirred Tank Reactor (CSTR) model, with

a classic example used to illustrate the different phenomena involved in reaction engineering. Two

different scenarios were simulated to analyze the transient behavior of the CSTR under different

coolant temperature perturbations. In the first case, a 10 K reduction in coolant temperature led to a

significant drop in reaction temperature and increase in reactant concentration. In the second case,

an increase of 5 K in coolant temperature resulted in oscillatory behavior, showcasing the reactor's

sensitivity to temperature changes. The presented simulation is consistent with reference values

from the literature, confirming the accuracy and reliability of the Xcos® model.

Key words: dynamics systems, open-source, MATLAB/simulink alternatives.

Luis Carlos Juárez-Martínez1*, Javier Tovar-Facio1, Rocío Anchondo-Granados1, Rosalía

Ruiz-Santos1, Anel Rocío Carrasco-Hernández1

1 Facultad de Ciencias Químicas, Universidad Autónoma de Chihuahua. Circuito Universitario S/N,

Campus UACH II, Chihuahua, Chih. 31125, México.

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Resumen

Comprender el comportamiento dinámico de los procesos químicos es esencial para el control de

procesos industriales, la mejora de la seguridad y la obtención de productos de calidad. Este trabajo

proporciona una guía accesible y práctica para estudiantes y educadores, demostrando el potencial

de Scilab/Xcos® como alternativa de código abierto a MATLAB/Simulink®, para la simulación

dinámica de procesos en la enseñanza de la ingeniería química. El trabajo se centra en el análisis de

un Reactor Continuo de Tanque Agitado (CSTR), utilizando un ejemplo clásico de la literatura para

ilustrar los distintos fenómenos involucrados en la ingeniería de reacciones cuando existen no

linealidades. Se simularon dos escenarios diferentes para analizar el comportamiento transitorio del

CSTR bajo distintas perturbaciones en la temperatura del refrigerante. En el primer caso, una

reducción de 10 K en la temperatura del refrigerante provocó una disminución significativa en la

temperatura de reacción y un aumento en la concentración del reactivo. En el segundo caso, un

incremento de 5 K en la temperatura del refrigerante resultó en un comportamiento oscilatorio,

evidenciando la sensibilidad del reactor a los cambios de temperatura. La simulación presentada es

consistente con los valores de referencia de la literatura, lo que confirma la precisión y confiabilidad

del modelo en Xcos® propuesto.

Palabras clave: sistemas dinámicos, código abierto, alternativas a MATLAB/simulink®.

1. Introduction

The design and operation of industrial plants to produce chemicals requires a solid

understanding of the dynamics systems. This field explores intricate mechanisms governing

chemical reactions with time varying behaviors, facilitating the anticipation, and regulation of

crucial variables like reaction rate, reaction conversion, and product selectivity. By understanding

the kinetics and thermodynamics involved, engineers can design efficient processes, decrease

production expenses, and mitigate environmental footprints. Moreover, process dynamics research

plays a crucial role in maintaining safety standards and products quality in the chemical industry,

while accelerating improvements in chemical processes (Shokry et al., 2020), automation

technologies (Shi et al., 2021), and process intensification (Baldea & Edgar, 2018).

In this respect, Simulink® a toolbox from MATLAB® has helped chemical engineering students at

many universities to learn dynamics and process control. Simulink® is a programming environment

characterized by its block-oriented architecture, making it well-suited for dynamic system modeling

and simulation. Its functionality extends to facilitating system-level design, automatic code

generation, and testing and verification embedded systems. A notable attribute of Simulink® is its

graphical editor and solvers, which enhance the intuitiveness and simplicity of modeling and

simulation tasks compared to conventional numerical coding methods (The MathWorks, 2025).

MATLAB/Simulink® has been used widely for chemical process control analysis. It is easy to find

research papers, tutorials and courses focused on the use of Simulink® for different process control

applications, such as: temperature control of heat exchangers (Jin et al., 2021), control of chemical

reactors (Muhammad et al., 2019) and distillation columns control (Minh, 2010). In addition, some

tutorials can be found at the MathWorks website (The MathWorks, 2025) and full material of

Dynamics and Control courses are available online (for example, Process Dynamics and Control by

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J. Hedenren (Hedengren, 2024) or Process Dynamics, Operations and Control by B. Johnston (MIT

OpenCourseWare, 2024)).

Despite the good features offered by MATLAB/Simulink®, the main disadvantage is related to

licensing cost, which could limit the access to this tool in low and lower middle-income countries.

Consequently, open-source alternatives represent an attractive option for dynamic system modeling

and simulation. Students and educators can find dynamics and control tools that can be used in the

Python programming language; however, these require a level of experience in using this language

or computational tools that students do not always have. Xcos® is a dynamic systems modeler and

simulator that can make up for the lack of programming experience. This powerful tool is available

with Scilab®.

Scilab® offers the benefit of being an open-source simulation tool with a user-friendly interface. It

encompasses numerous mathematical functions and allows the integration of programs from other

languages, such as C++ and Fortran. Additionally, it features a control-oriented toolbox known as

Xcos®, which employs a block-oriented programming approach. Xcos® enables the creation of

mathematical models graphically, utilizing fundamental computing blocks in discrete and

continuous time domains (Dassault Systèmes, 2024).

The Autonomous University of Chihuahua (Universidad Autónoma de Chihuahua, UACH) in

Mexico, offers a process dynamics and control course at the ninth semester (the last semester) in the

undergraduate Chemical Engineering and Food Engineering programs. This subject is a chemical

engineering course commonly offered in other universities worldwide at the end of the program, as

mentioned by Moodley (Moodley, 2020).

Although, the exploration of chemical reactor dynamics starts with the chemical reactor design

course during the third year of the chemical engineering program at the UACH, the process

dynamics and control course is focused on understanding the dynamic performance and control

strategies of different process units such as: mixing tanks, separation columns, heat exchangers,

boilers, and chemical reactors. An important part of the course is that the students gain knowledge

about transient behavior of the processes to evaluate different scenarios that can be found in industry

related to normal and abnormal operation conditions. To achieve this, the use of computational tools

for modeling and simulating chemical processes in dynamic states is both crucial and necessary in

the classroom. The same assertion has been made by other authors such as, Moodley (2020), Vieira

et.al. (2019), and Henrique et.al. (2018).

According to Vieira et.al. (2019), Xcos® is an excellent option for studying dynamic simulations.

However, there is a lack of research papers focused on training and demonstrating the utility of

Xcos® for academic purposes, with most information concentrating on process control.

Hence, the aim of this paper is to present a useful guide for students and professors interested in the

field of chemical process dynamics by using the Scilab/Xcos® programming environment. Also, the

paper brings a comprehensive derivation of the dynamic mass and energy balance equations

involved in the system, by solving a classical non-linear Continuous Stirred Tank Reactor (CSTR)

dynamics example, described in the workhorse book of Process Dynamics and Control written by

Seaborg, et.al. (2016).

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To facilitate reading, the paper is divided into the following sections: in Section 2 an example of

dynamic assessment process is presented, and mathematical model and implementation in Xcos® is

also presented. In section 3, the simulations results can be found. Finally, the conclusions are given

in section 4.

2. Materials and Methods

The study of continuous stirred-tank reactors in chemical engineering programs is of a great

importance because they are widely used in different industrial applications, such as:

pharmaceuticals (Hu, 2021), polymers manufacturing (Wang et al., 2018), in biotechnology to treat

petroleum wastewater (Pugazhendi et al., 2017), and some novel applications such as clean hydrogen

production (Ghimire et al., 2015).

Another important characteristic is that CSTR models are simpler than other reactors such as tubular

and packed-bed reactors. Hence, the study of continuous stirred-tank reactors offers a practical

means to demonstrate modeling principles for chemical reactors in an educational setting.

2.1. Model description

For this study, a non-isothermal continuous stirred-tank reactor was modeled and simulated,

adapted from (Seborg et al., 2016). In this setup, a liquid-phase chemical reaction is studied, where

species A irreversibly transforms into species B. The reaction equation can be represented as follows:

   Eq. (1)

An assumption is that the reaction rate is determined by the concentration of component A,

following first-order reaction kinetics (Eq. 2).

   Eq. (2)

Where 󰇛󰇜 is the reaction rate, 󰇛󰇜 is the reaction rate constant, and 󰇛󰇜 is the molar concentration of

the reactant .

For single-phase reactions, it can be assumed that the rate constant depends only on the reaction

temperature that it can be described by the Arrhenius equation, expressed by Eq. (3).

󰇛󰇜  󰇡

󰇢 Eq. (3)

Where 󰇛󰇜 is the frequency factor, 󰇛󰇜 is the activation energy, 󰇛󰇜 is the ideal gas constant, and 󰇛󰇜

is the absolute reaction temperature.

Regarding Eqs. (2) and (3), these are classified as semi-empirical relations since the parameters 󰇛󰇜

and 󰇛󰇜 are obtained by fitting experimental data.

In Fig. 1, the schematic diagram of the CSTR studied in this work is shown. As can be seen, only

component  is fed to the reactor at a certain flow rate (), at temperature () with a molar

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concentration 󰇛󰇜. The outlet stream exits the reactor at a flow rate of (), at the reaction

temperature () with a concentration of (). To keep reaction at the desired temperature (nominal

value), a cooling fluid is fed through the cooling coil at temperature ().

Figure 1. Continuous Stirred Tank Reactor adapted from Seaborg et.al. (2016).

Figura 1. Reactor Continuo de Tanque Agitado adaptado de Seaborg et al. (2016).

2.2 Mathematical model

This section provides the dynamic derivation of the mass and energy balance equations based

on fundamental principles.

Mass balance

The derivation of the ordinary differential equation that describes the accumulation rate of the

chemical reactants is based on several ideal assumptions (Seborg et al., 2016):

 A complete mixing is considered.

 Feed and products have constant densities, denoted as 󰇛󰇜

 Reaction takes place at constant volume 󰇛󰇜.

Under the previous assumptions, the general mass balance equation can be expressed in the form

shown by Eq. (4).



  󰇗   󰇗  󰇗 Eq. (4)

The derivative term 󰇡

 󰇢 in Eq. (4) represents the material accumulation in the system, 󰇛󰇗 󰇜 and

󰇛󰇗 󰇜 are the inlet and outlet mass flow rates, respectively, (󰇗󰇜 is the generation rate of any chemical

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species due to chemical reactions. Since 󰇛󰇜 and 󰇛󰇜 are constants, then the mass () and mass flow

rate (󰇗 ) can be expressed in the form of Eqs. (5) and (6), respectively.

     Eq. (5)

󰇗     Eq. (6)

On the other hand, the rate of generation and consumption of the reactant (A, in this reaction) is

based on reaction kinetics; see Eq. (2). Assuming a well-mixed reactor condition, the reaction rate

󰇛󰇜 does not change with respect to the reactor position. Then, the generation rate of any species can

be expressed in the form of Eq. (7).

󰇗  Eq. (7)

For this example, a first-order reaction is considered with respect to A; hence, the kinetic equation is

given by Eq. (8)

  Eq. (8)

Substituting Eqs. (5–8) into Eq. (4) leads to Eq. (9):

󰇛󰇜

    Eq. (9)

Where 󰇛󰇜 and 󰇛󰇜 are the inlet and outlet volumetric flows, respectively.

Finally, since󰇛󰇜 and 󰇛󰇜 are constants, the inlet and outlet volumetric flow rates ( and ) are equal,

and this assumption must be satisfied at all the time (Seborg et al., 2016).

With the previous assumptions, the unsteady-state component balance for specie A (in molar units)

is described by Eq. (10).



    Eq. (10)

Energy balance

To derive the energy balance equation, the following assumptions are needed (Seborg et al., 2016):

 The thermal capacitance of the coolant and the wall of the heat transfer tubes is negligible

compared to the thermal capacitance of reaction species inside the reaction tank.

 Uniform coolant temperature distribution is considered, and it is denoted as 󰇛󰇜. Therefore,

any temperature changes in coolant temperature when passes through the tubes is

neglected.

 The heat of mixing is negligible compared to the reaction enthalpy.

 Thermal losses to the ambient and shaft work are neglected.

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According to the assumptions, the dynamic general energy balance equation is presented in Eq. (11).



  󰇗  󰇗  󰇗 󰇗 Eq. (11)

Where derivative term 󰇡

󰇢represents the energy accumulation in the system, 󰇛󰇗󰇜 and (󰇗󰇜 are

the energy flow that enters and exits the system, and 󰇛󰇗󰇜 and (󰇗) is the rate of reaction heat.

To account the energy accumulation in the system, and the energy flow through the system, Eqs.

(12-14) are used in terms of density, volume and enthalpy.

          Eq. (12)

󰇗  󰇗         Eq. (13)

󰇗  󰇗          Eq. (14)

Where 󰇛󰇜 is the reaction mass, 󰇛󰇗 󰇜 and (󰇗 󰇜are the inlet and outlet mass flow rates, and (󰇜,

󰇛󰇜 and 󰇛󰇜 are the inlet and outlet specific enthalpies.

The rate of heat generation (󰇗) due to the chemical reaction is accounted by Eq. (15), and the heat

transfer between the reaction and the coolant is expressed by Eq. (16).

󰇗 󰇛󰇜 Eq. (15)

  󰇛 󰇜 Eq. (16)

Where 󰇛󰇜 is the change of enthalpy of reactants and products, 󰇛󰇜 is the reaction rate at

constant volume, 󰇛󰇜 represents the overall heat transfer coefficient, 󰇛󰇜 denotes the heat transfer

area, 󰇛󰇜 and 󰇛󰇜 are the average coolant and reaction temperatures, respectively.

Substituting Eqs. (12-16) in Eq. (11), the energy balance equation takes the form of Eq. (17), where

specific enthalpies can be written as the product of 󰇛  󰇜.



   󰇛󰇜󰇛 󰇜 Eq. (17)

2.3 Model implementation in Xcos®

The intuitive graphical editor in Xcos® simplifies the representation of mathematical models

through block diagrams, where each block corresponds to a predefined function or a user-defined

custom function. These blocks connect seamlessly within the interface, enabling straightforward

system design and analysis (Dassault Systèmes, 2024). In this section a brief description of the blocks

used on the CSTR model is presented.

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Xcos® Blocks description

To guide readers in creating the block diagram shown in Fig. 2, Table 1 provides a

description of each object used in this work. The block descriptions are available in the palette browser

within Xcos®.

CSTR model

The CSTR model, which includes Eqs. (3, 10, and 17), corresponds to a coupled set of

differential and algebraic equations. Each equation was implemented in separate subsystems

(SUPER_f blocks) to improve the understanding of the coupled system and facilitate the manipulation

of the variables involved, as shown in Fig. 2.

The illustration of Fig. 2 shows the interaction between subsystems. The initial guess is based on the

steady-state conditions for reaction temperature 󰇛󰇜 and specie A concentration 󰇛󰇜. Under these

conditions, the reaction rate constant 󰇛󰇜 is computed within the Arrhenius Equation Subsystem and

then passed to the Mass and Energy Balance Subsystems to update the reaction temperature and

concentration. This process repeats multiple times until the simulation is complete. The system

integrates user-defined functions with built-in Xcos blocks for mass and energy balances. The mass

balance equation is solved through a dedicated subsystem (highlighted in magenta), while the

energy balance is handled in a separate module (in red). The data flow arrows represent the

directional exchange of variables (e.g., concentration, temperature) between the subsystems and the

main function block.

Figure 2. Diagram of the coupled system implemented in Xcos® for the dynamic simulation of a Continuous

Stirred Tank Reactor (CSTR).

Figura 2. Diagrama del sistema acoplado implementado en Xcos® para la simulación dinámica de un reactor

continuo de tanque agitado (CSTR).

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Table 1. Description of the blocks used from palette browser in Xcos®.

Tabla 1. Descripción de los bloques utilizados del palette browser en Xcos®.

Block name

Description

This block is an integrator. The output  is the integral of the

input at the current time step .

Set constant value block. This block allows setting a numeric

constant value.

This block performs addition or subtraction on scalar, vector or

matrix inputs. The input datatype is set with the datatype

parameter. The number of inputs or sign vector parameter defines

the number of inputs and operation. For a single vector's input,

the block collapses the elements of the vector. Vectors/matrices

inputs must have the same size.

This block computes element-wise multiplication or division of

its vector inputs. The number of inputs and operation are

specified with the number of inputs or sign vector parameter.

To multiply/divide the input , set in this parameter a vector

with  (multiply) or  (divide) for the input .

The unique output of this block generates a regular train of

events that are scheduled by parameter period in seconds. The

starting date of events generation can be set in seconds with the

Initialization Time parameter.

The Scope block displays its input with respect to simulation

time. Both axes have a common range. The Scope allows you to

adjust the amount of time and the range of input values

displayed. It has the feature to scale the graph at runtime.

This block opens a new Xcos® window for editing a new block

diagram. This diagram describes the internal functions of the

super block. Super block inputs and outputs (regular or event)

are designated by special (input or output) blocks.

This block can realize any type of Scicos block. The function of

the block is defined interactively using dialogue boxes and in

Scilab® language. During simulation, these instructions are

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interpreted by Scilab®; the simulation of diagrams that include

these types of blocks is slower

Simulation parameters

The effect of sudden changes in coolant temperature (), was analyzed by replicating both

positive and negative step changes in (), as reported in Seborg et al. (2016).

Table 2 presents key parameters and nominal operating conditions for the Continuous Stirred Tank

Reactor. The system is described by ordinary differential equations (ODEs), with two state variables:

reactant concentration󰇛󰇜and reactor temperature 󰇛󰇜. The cooling water temperature 󰇛󰇜 serves

as the manipulated variable.

Table 2. Simulation parameters (Seborg et al., 2016).

Tabla 2. Parámetros de simulación (Seborg et al., 2016).

Parameter

Symbol

Value

Units

Activation energy



72,750



Arrhenius pre-exponential







Gas constant



8.314

 

Reactor volume



100

Density



1000



Heat capacity



0.239

  

Enthalpy of reaction



-50,000



Heat transfer coefficient



50,000

  

Feed flowrate



100



Feed concentration



1.0



Feed temperature



350



Initial concentration



0.5



Initial temperature



350



Coolant temperature



300



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Mass balance equation subsystem configuration

To implement the mass balance equation in Xcos® environment, Eq. (10) needs to be

rearranged as follows: the volume divides the equation to have only the derivative term at the left-

hand side of the equation. As a result, both terms on the right-hand side of Eq. (10) are also divided

by the volume (V), yielding a new equation, given in Eq. (18).



 

   Eq. (18)

The block diagram for Eq. (18) that is within the subsystem called Mass Balance Equation, is presented

in Fig. 3. The nominal parameters 󰇛󰇜, 󰇛󰇜, and 󰇛󰇜 are modeled using constant blocks since their

values remain unchanged during the simulation. To declare their respective value, the set context box

that can be found on the simulation tab was used. About algebraic operations, they are represented

by their respective addition, subtraction, multiplication and division blocks. To help readers

understand how these operations were performed, labels were added to the corresponding blocks

to indicate the type of computation carried out, see Fig. 3.

Figure 3. Block diagram in Xcos® representing the dynamic implementation of the mass balance equation for

the Continuous Stirred Tank Reactor (CSTR).

Figura3. Diagrama de bloques en Xcos® que representa la implementación dinámica de la ecuación de

balance de masa para el Reactor de Tanque Agitado Continuo (CSTR).

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In Fig. 3 is shown the problem model. The model incorporates key input parameters such as flow

rate (), reactor volume (), and feed concentration (). The expression 󰇛󰇜󰇛󰇜 represents

the convective mass transport, and the term 󰇛󰇜 accounts for the first-order reaction kinetics. The

output concentration () is obtained through numerical integration and plotted in real time using

the Scope block.

The set context box allows variable definition and mathematical operations to simplify variable

manipulation, see Fig. 4.

Figure 4. Variable definition in set context for the mass balance equation.

Figura 4. Definición de variables en set context para la ecuación de balance de masa.

Finally, the integrator is set up with the initial condition  . This action can be done by

clicking on the integrator block and typing the desired value on the initial condition blank space, see

Fig. 5.

Figure 5. Initial condition set up for the  integrator block.

Figura 5. Configuración de la condición inicial para el bloque integrador .

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Energy balance equation subsystem

Analogous to the mass balance equation, Eq. (17) must be solved to isolate the derivative

term. To achieve this, Eq. (17) is divided by the product of 󰇛󰇜, resulting in a new equation, Eq.

(19).



 

󰇛 󰇜󰇛󰇜

 

󰇛󰇜 Eq. (19)

In Fig. 6, the block diagram to solve Eq. (19) is presented. In this case the nominal parameters were

also introduced as constant blocks, such as:  and .

Figure 6. Xcos® block diagram implementing the energy balance equation for the Continuous Stirred Tank

Reactor (CSTR).

Figura 6. Diagrama de bloques de Xcos® que implementa la ecuación de balance de energía para un Reactor

de Tanque Agitado Continuo (CSTR).

In Fig. 6 is shown how the model dynamically calculates the reactor temperature () by integrating

contributions from convective heat exchange 󰇛󰇜󰇛 󰇜, heat generated by the reaction

() and heat transfer with the cooling medium (). The values of the nominal

constant parameters were also set using the set context box (see Fig. 7).

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Figure 7. Variable definition in set context box for energy balance equation.

Figura 7. Definición de variables en set context para la ecuación de balance de energía.

For the reaction temperature integrator, the initial condition was set to 350 K, as shown in Fig. 8.

Figure 8. Initial condition set up for reaction temperature integrator block.

Figura 8. Configuración de la condición inicial para el bloque integrador de temperatura de reacción.

Arrhenius equation block

The Arrhenius equation is an exponential function that depends on temperature (Eq. 3). Each

time the reaction temperature changes, the reaction rate constant must be recalculated. In Xcos®,

solving this equation requires utilizing the user-defined function sfunc_block_m.

Double-clicking the sfunc_block_m opens a new configuration window. The first two entries, input

port sizes and output port sizes, should be set to [1,1] and [1,1], respectively. This configuration

indicates that a single input variable, the reaction temperature (T) from the Energy Balance

Subsystem enters the block, while a single output variable, the specific rate constant, exits. Once the

input and output port sizes are defined, click OK to proceed.

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The previous action displays a new box where the function is introduced as follows: on the top of

the box the name of the function is written as Arrhenius Equation, then the inlet variable 󰇛󰇜 that

comes from the Energy Balance equation is defined as Global T. If more input variables are needed,

all of them must be settled as global variables.

To solve a time-dependent function in Xcos®, it must be expressed in the form    . The Arrhenius

equation is then solved in the form of Eq. (20).

 󰇛󰇜  󰇡

󰇢 Eq. (20)

Where  󰇛󰇜;

 ;

 ;

 ;

 

Once the function is defined, click ok to continue. The new box, the global variable 󰇛󰇜 is rewritten

for initialization and click ok. If more input variables are needed, they must be declared here for their

respective initialization.

The fourth box is used to create additional commands such as: create graphics, export data

open/close graphics, etc. In this case the box has been left in blank, due to additional instructions are

not necessary. Finally, the last box can be used to define restriction for input, output and state

variables if needed, but in this case, it was also left in blank. The whole process of the user-defined

function configuration is depicted in Fig. 9.

Figure 9. The Arrhenius equation configuration using the sfunc_block_m.

Figura 9. Configuración de la ecuación de Arrhenius utilizando el sfunc_block_m.

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3. Results and discussion

To analyze the transient behavior of the CSTR model presented in the previous section, two

different scenarios were simulated as follows: for the first case, enhanced cooling was simulated by

modifying  from 300 K to 290 K. The second case focuses on reducing the cooling rate,

accomplished by increasing  from 300 K to 305 K. For both cases, the simulation time was set to

10 minutes.

In the first case, decreasing the coolant temperature to 290 K has two major effects. First, the reaction

temperature drops by approximately 37 K, reaching a new steady-state value of 312.6 K. Second, the

molar concentration of the reactant 󰇛󰇜 increases from 0. mol/L to a new steady-state value of 0.952

mol/L.

For the second simulation, when the cooling jacket temperature is set at 305 K, the CSTR exhibits

sustained oscillations due to the exothermic nature of the reaction and its strong temperature

dependence. As the temperature spikes, the reaction accelerates quickly consuming reactant A. Once

the concentration drops, heat generation decreases, allowing the reactor to cool. The continuous feed

then restores the amount of A, initiating a new cycle.

This nonlinear feedback between reaction kinetics and heat removal leads to self-sustained

oscillations in temperature and concentration. As explained by Seborg et al. (2016), such behavior is

not unusual in chemical reactors, particularly under marginal or critical operating conditions. Small

variations in parameters like the coolant temperature, inlet concentration, or activation energy can

drastically shift the system from steady-state to oscillatory or even unstable regimes.

Figure 10. Reactor temperature response due to coolant temperature changes (), nominal temperature of 300

K. Left side represents the reference results from Seborg et al. (2016) and the right side shows the results

obtained with Xcos®.

Figura 10. Respuesta de la temperatura del reactor debido a cambios en la temperatura del refrigerante (Tc),

con una temperatura nominal de 300 K. El lado izquierdo representa los resultados de referencia de Seborg et

al. (2016), y el lado derecho muestra los resultados obtenidos con Xcos®.

According to this, the results obtained with Xcos® align with the reference values, confirming that

the CSTR model simulated in this study accurately represents the reference model reported by

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Seborg et al. (2016). Figs. 10 and 11 present a graphical comparison between the reference results and

the previously discussed simulations.

Figure 11. Concentration response due to coolant temperature changes (), nominal temperature

300 K. Left side represents the reference results from Seborg et al. (2016) and the right side shows

the results obtained with Xcos®.

Figura 11. Respuesta de la concentración debido a cambios en la temperatura del refrigerante (),

temperatura nominal de 300 K. El lado izquierdo representa los resultados de referencia Seborg et

al. (2016), y el lado derecho muestra los resultados obtenidos con Xcos®.

4. Conclusions

This study explored the use of Xcos® for solving dynamic chemical engineering problems.

Specifically, the dynamics of a continuous stirred tank reactor (CSTR) were analyzed, including

model description, mathematical formulation, and Xcos® implementation.

Although, the use of Scilab/Xcos® is not new in research or academia, most of the research papers

are focused on dynamics for control purposes of specific problems in which it is assumed that

readers have certain knowledge on the topic to understand both mathematical models and

implementation. Hence, the structure of this paper was intended to be a practical guide describing

the steps to follow for dynamic modeling and simulation with Xcos®, especially for students and

educators interested in dynamic systems.

The simulator was validated using a well-known example from Seborg et al. (2016), a widely used

textbook in process dynamics and control courses. The simulation results closely matched the

reference values, confirming the accuracy of the model. Therefore, this model can serve as a reliable

reference for educational projects and research activities related to chemical reaction engineering.

Currently, our research group is developing different unit operation simulators that are commonly

studied in chemical engineering programs. The research group aims to offer a wide range of models

for analyzing full plant process dynamics and supports the teaching process using open-source tools.

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Hence, we encourage readers to contact the corresponding author for access to the simulator or for

further guidance on how to implement the models discussed in the paper. The authors are open to

providing support for specific simulations, answering technical questions, and offering insights on

adapting the simulator to different case studies or research needs. Reaching out can help ensure the

correct use of the simulator and facilitate collaboration on improvements or extensions.

Acknowledge

The research group FCQ-GI-23-001 acknowledge the Secretary of Research and Postgraduate

Studies of the Faculty of Chemical Sciences, Universidad Autónoma de Chihuahua, for the support

to establish the research group.

Declaration of Competing Interest

The authors declare that there are no known financial conflicts of interest or personal

relationships that could have influenced the research presented in this paper.

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